On the Dual and Inverse Problems of Scheduling Jobs to Minimize the Maximum Penalty

• Main Authors: Alexander A. Lazarev, Nikolay Pravdivets, Frank Werner
• Format: Article
• Language: English
• Published: MDPI AG 2020-07-01
• Series: Mathematics
• Subjects: single-machine scheduling; minimization of maximum penalty; dual problem; inverse problem; branch and bound
• Online Access: https://www.mdpi.com/2227-7390/8/7/1131
• ISSN: 2227-7390

In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial time. Since the dual problem gives a lower bound on the optimal objective function value of the original problem, we use the optimal function value of a sub-problem of the dual problem in a branch and bound algorithm for the original single-machine scheduling problem. We present some initial computational results for instances with up to 20 jobs.